Interactive multiple-choice quiz: اختبار الرياضيات ريفيل الوحدة العاشرة
يتناول هذا الاختبار مفاهيم الإحصاء والاستدلال الرياضي من خلال دراسة العينات العشوائية وأنواعها مثل العينة العشوائية البسيطة والمنتظمة. كما يتطرق الاختبار إلى تحليل البيانات باستخدام الرسوم البيانية كالمخططات النقطية (Dot Plots) ومخططات الصندوق والشاربين (Box Plots)، وكيفية حساب مقاييس النزعة المركزية مثل الوسيط والمتوسط الحسابي، ومقاييس التشتت مثل المدى والانحراف المتوسط المطلق (MAD). تهدف هذه الأسئلة إلى تطوير قدرة الطالب على التنبؤ بنتائج المجتمع بناءً على بيانات العينات ومقارنة مجموعات البيانات المختلفة.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
To determine whether students think a new school library is needed, a computer generates a list of 100 random students and they are surveyed. Which method is used?
Explanation
A computer generating a list from the entire population where every student has an equal chance of being selected is the definition of a simple random sample.
Question 2
Points: 1
A member of the cafeteria staff asks every fifth student leaving the cafeteria to rank 5 entrees. She finds pizza is a favorite. Is this a valid sampling method?
Explanation
Selecting every nth individual (in this case, every fifth) from a population is called systematic random sampling, which is generally unbiased.
Question 3
Points: 1
20 people leaving a restaurant are surveyed at random; 8 say they usually order dessert. What percent say they usually do NOT order dessert?
Explanation
If 8 out of 20 order dessert, then 20 - 8 = 12 do not. The percentage is \(\frac{12}{20} = 0.6 = 60\%\).
Question 4
Points: 1
A school librarian surveys 25 students. predict how many science fiction books she will need to purchase if 125 students participate in book club next year.
Explanation
Based on the table, 6 out of 25 students chose Science Fiction. To predict for 125 students: \(\frac{6}{25} \times 125 = 6 \times 5 = 30\).
Question 5
Points: 1
If a school district has 5,000 middle school students next year, about how many plan to buy lunch 1-2 days a week based on the pie chart (37%)?
Explanation
The pie chart shows 37% for 1-2 days. \(37\% \text{ of } 5000 = 0.37 \times 5000 = 1850\).
Question 6
Points: 1
Of 240 checked boxes of crayons, 2 did not pass inspection. How many boxes out of 12,000 should the crayon company expect to not pass inspection?
Explanation
The failure rate is \(\frac{2}{240} = \frac{1}{120}\). For 12,000 boxes, the expectation is \(\frac{1}{120} \times 12000 = 100\).
Question 7
Points: 1
The dot plot in the first image displays data from 14 random samples. Each dot represents the mean number of sports played per year by students in that sample. Which number best represents the mean number of sports played by middle school students overall?
Explanation
Looking at the dot plot of sample means, the data is centered around 2.5, which represents the mean of the sample means and is the best estimate for the population mean.
Question 8
Points: 1
Find and interpret the variability in the distribution based on the range of the sample means.
Explanation
The range is the difference between the maximum and minimum values. Max = 3.5, Min = 1. Range = 3.5 - 1 = 2.5.
Question 9
Points: 1
A student examines the dot plot below, which shows the "Means of Samples." The student states that the plot contains samples of size 30. Find the student's mistake and choose the correct correction.
Explanation
In a dot plot of sample means, each dot represents one sample (its mean). There are 30 dots, meaning 30 samples were taken, but this doesn't tell us how many individuals were in each of those samples.
Question 10
Points: 1
A student claims that if 50% of data is below the median and 50% is above, the data must be symmetric. What is the student's error?
Explanation
By definition, the median is the middle value. While 50% of data is always above and below it, the distribution of those values could be skewed (not symmetric).
Question 11
Points: 1
Based on the box plots for City A and City B:
- City A: Median = 6 days.
- City B: Median = 5 days.
For which city is it more likely that a randomly selected month will have 6 or more rainy days?
Explanation
Since City A's median is 6, we know that 50% of the data points are at or above 6. City B's median is only 5, so more than 50% of its data is below 6.
Question 12
Points: 1
Based on the double dot plot showing weights in pounds:
- Housecats: Range 9-13 lbs, Median at 11 lbs.
- Small Dogs: Range 6-12 lbs, Median at 9 lbs.
Which of the following is a correct inference about the data?
Explanation
Comparing the medians, housecats (11 lbs) have a higher center than small dogs (9 lbs).
Question 13
Points: 1
The double dot plot shows sample weights of two breeds of dogs (Beagle and Dachshund). The table provides the Mean and Mean Absolute Deviation (MAD) for each breed:
- Beagle Mean: 20.5 lb, MAD: 1.36
- Dachshund Mean: 26.5 lb, MAD: 1.36
How many measures of variability separate the means of the samples?
Explanation
The difference between the means is 26.5 - 20.5 = 6.0. To find the measures of variability separation, divide by the MAD: \(\frac{6.0}{1.36} \approx 4.41\).
Question 14
Points: 1
A graph shows the mean of 15 random samples of 20 students each. What is the best estimate of the mean number of hours spent per night doing homework of the population?
Explanation
The dots (sample means) are clustered around the value 2 on the 'Hours Per Night' scale, making 2 the best estimate for the population mean.
Question 15
Points: 1
A grocery store conducts a random survey of its customers and finds that 78% would sign up for a rewards program if it were offered. If the rewards program is rolled out this weekend and there are 1,550 customers, how many of them would you expect to sign up for the program?
Explanation
Expected value is calculated by multiplying the percentage by the total population: 0.78 × 1550 = 1209.
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